In control systems, the term “instability” commonly refers to the presence of an oscillation with a continuously-increasing amplitude. As used herein, however, the term “instability” refers to the presence of an undesirable amplitude of at least one oscillatory mode of a system. This undesirable amplitude may be intermittent, constant or continuously increasing.
Oscillations can result from a variety of causes. An oscillation may be the result of resonance, where the mode is excited at its natural frequency in a closed or open loop system. Resulting is a linear instability
An oscillation may be the result of free vibration with negative damping, where controller stimulus frequency is unrelated but supplies power. Resulting is a self-excited vibration.
In a control system that applies a stimulus to an object, an oscillation may be caused by a non-linearity such as friction or backlash. Resulting is a limit cycle oscillation. Unlike oscillations caused by linear instabilities, a limit cycle oscillation is saturated and doesn't grow in amplitude. Total phase lag around a control loop that is limit-cycle oscillating is exactly 360 degrees and loop gain is unity.
The onset of instability due to a limit cycle or other oscillation is difficult to ascertain in a control system having a single channel. The difficulty is even greater in a control system having multiple channels due to the difficulty in identifying the channel that caused the initial instability. Moreover, one unstable channel can cause numerous channels to become unstable.
There is a need to quickly detect and control instabilities caused by limit cycle oscillations and other oscillations having undesirable amplitudes.